{"paper":{"title":"A consequence of the growth of rotation sets for families of diffeomorphisms of the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Salvador Addas-Zanata","submitted_at":"2018-01-30T01:43:27Z","abstract_excerpt":"In this paper we consider $C^\\infty $-generic families of area-preserving diffeomorphisms of the torus homotopic to the identity and their rotation sets. Let $f_t:\\rm{T^2\\rightarrow T^2}$ be such a family, $\\widetilde{f}_t:\\rm I\\negthinspace R^2 \\rightarrow \\rm I\\negthinspace R^2$ be a fixed family of lifts and $\\rho (\\widetilde{f}_t)$ be their rotation sets, which we assume to have interior for $t$ in a certain open interval $I.$ We also assume that some rational point $(\\frac pq,\\frac rq)\\in \\partial \\rho (\\widetilde{f}_{\\overline{t}})$ for a certain parameter $\\overline{t}\\in I$ and we want"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09820","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}